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1. Find the length of the curves: a) r(t) = (t, 3 cos t, 3 sin t ), -5 ≤ t ≤ 5 b) r(t) = √ēti + e¹j+e-¹k, 0≤ t ≤ 1 = 2y and the surface 3z = xy. Find c) Let C be the curve of the intersection of the parabolic cylinder x² the exact length of C from the origin to the point (6,18,36)

1. Find the length of the curves: a) r(t) = (t, 3 cos t, 3 sin t ), -5 ≤ t ≤ 5 b) r(t) = √ēti + e¹j+e-¹k, 0≤ t ≤ 1 = 2y and the surface 3z = xy. Find c) Let C be the curve of the intersection of the parabolic cylinder x² the exact length of C from the origin to the point (6,18,36)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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show full & complete procedure HANDWRITTEN only. Please answer parts a), b) & c). Note they are subparts of the same question. Note you need to use Gauss' Divergence Theorem 

Gauss' (Divergence) Theorem 1. Find the length of the curves: a) r(t) = (t, 3 cos t, 3 sin t ), -5 ≤ t ≤ 5 b) r(t) = √ēti + eºj + e¯ªk, 0 ≤ t ≤1 c) Let C be the curve of the intersection of the parabolic cylinder x² = 2y and the surface 3z = xy. Find the exact length of C from the origin to the point (6,18,36)
Transcribed Image Text:Gauss' (Divergence) Theorem 1. Find the length of the curves: a) r(t) = (t, 3 cos t, 3 sin t ), -5 ≤ t ≤ 5 b) r(t) = √ēti + eºj + e¯ªk, 0 ≤ t ≤1 c) Let C be the curve of the intersection of the parabolic cylinder x² = 2y and the surface 3z = xy. Find the exact length of C from the origin to the point (6,18,36)
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